We had a Cordyline in the garden and in about 12 years it grew from a cute plant to a 10 feet tall tree. It had to go to make way for a summerhouse and it was hard work to remove it.

I cut off the top growth and dug around the roots which were fibrous and not very extensive. I was then able to pull it over with ropes and cut the trunk up. That left a stump in the hole about 30 inches tall. The wood was dense, sappy and extremely heavy. I had to use a sheet of wood as a ramp and by hauling on ropes two of just about managed to pull it out of the hole.

What I am saying is: even with the size of the Cordyline in the photo, expect it to be heavy to move, especially with a good rootball attached. Good luck.